KPerkins2011.Conductivity

8/9/2019 KPerkins2011.Conductivity

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Measurement and Modeling ofUnsaturated Hydraulic Conductivity

Kim S. PerkinsUnited States Geological Survey

United States of America

1. Introduction

The unsaturated zone plays an extremely important hydrologic role that influences waterquality and quantity, ecosystem function and health, the connection between atmosphericand terrestrial processes, nutrient cycling, soil development, and natural hazards such asflooding and landslides. Unsaturated hydraulic conductivity is one of the main propertiesconsidered to govern flow; however it is very difficult to measure accurately. Knowledge ofthe highly nonlinear relationship between unsaturated hydraulic conductivity (K) and

volumetric water content () is required for widely-used models of water flow and solutetransport processes in the unsaturated zone. Measurement of unsaturated hydraulicconductivity of sediments is costly and time consuming, therefore use of models thatestimate this property from more easily measured bulk-physical properties is common. Inhydrologic studies, calculations based on property-transfer models informed by hydraulicproperty databases are often used in lieu of measured data from the site of interest. Relianceon database-informed predicted values with the use of neural networks has becomeincreasingly common. Hydraulic properties predicted using databases may be adequate insome applications, but not others.This chapter will discuss, by way of examples, various techniques used to measure and

model hydraulic conductivity as a function of water content, K(). The parameters that

describe the K() curve obtained by different methods are used directly in Richardsequation-based numerical models, which have some degree of sensitivity to thoseparameters. This chapter will explore the complications of using laboratory measured orestimated properties for field scale investigations to shed light on how adequately the

processes are represented. Additionally, some more recent concepts for representingunsaturated-zone flow processes will be discussed.

2. Hydraulic conductivity measurement

The most direct and most generally reliable measurements of unsaturated hydraulicconductivity are from steady-state flow methods. These methods are seldom applied,however. In the simple gravity-driven implementations they have serious drawbacks:limitation to the wettest soil conditions, and slowness, sometimes requiring months for a

singleK measurement. The Steady-State Centrifuge (SSC) method, used to measureK() forthe samples presented here, extends the range to lower steady-stateK measurements by at


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Hydraulic Conductivity Issues, Determination and Applications420

least three orders of magnitude, and allows at least six points of the unsaturatedK relation

with to be characterized for a pair of samples in about five days (Nimmo and others, 2002).

The steady state centrifuge (SSC) method used to measure K() on 40 samples from theIdaho National Laboratory is the Unsaturated Flow Apparatus1 (UFA) version (Conca and

Wright, 1998; Nimmo et al., 2002) of the method originally developed by Nimmo et al.(1987). The core samples were sub-cored in the laboratory using a mechanical coring deviceinto a 4.9-cm-long, 3.3-cm-diameter retainer designed specifically to fit into the buckets ofthe UFA centrifugal rotor.The SSC method requires that steady-state conditions be established within a sample undercentrifugal force. Steady-state conditions require application of a constant flow rate and aconstant centrifugal force for sufficient time that both the water distribution and the waterflux within the sample become constant. When these conditions are satisfied, Darcys law

relatesK to and matric pressure () for the established conditions as follows:

2d

q K C r dr

(1)

where q is the flux density (cm/s), C is a unit conversion factor of 1 cm-water/980.7dyne/cm2(1 cm of water is equal to a pressure of 980.7 dyne/cm2and 1 dyne is equal to 1 g

cm/s2), is the density of the applied fluid (g/cm3), is the angular velocity (rad/s), and ris the radius of centrifugal rotation (cm). If the driving force is applied with the centrifuge

rotation speed large enough to ensure that d/dr


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Measurement and Modeling of Unsaturated Hydraulic Conductivity 421

allows for rapid measurement at low Ksat values using the equation from Nimmo et al.(2002)

2 2

2 2

2ln

f b

sat

f i i b

gz raLK A g t t gz r

(3)

where ais the cross sectional area of the inflow reservoir (cm2), Lis the sample length (cm),Ais the cross sectional area of the sample (cm2), tis time (initial and final), zis the height ofwater above the plane in which the sample rotates (initial and final height, cm), and br is the

position of the bottom of the sample (cm).

3. Hydraulic conductivity estimation

When direct measurements ofK() are not obtainable it is possible to estimate using more

easily measured properties such as particle size distributions. To estimate K), and Ksatparameters (measured and modeled) were combined with Mualems (1976) capillary-bundlemodel, one of the most widely used K) models available. Mualems model infers a pore-size distribution for a soil from its curve based on capillary theory, which assumes thata pore radius is proportional to the value at which that pore drains. Mualems modelconceptualizes pores as pairs of capillary tubes whose lengths are proportional to their radii;the conductance of each capillary-tube pair is determined according to Poiseuilles law2. Inthis formulation,K() is defined as

r satK K K (4)

where Kr() is relative hydraulic conductivity. To computeK() for the whole medium, theconductance of all capillary-tube pairs is integrated as

2

0

0

1

( )

1

( )

sat

Lr e

d

K Sd

(5)

Where L is a dimensionless parameter interpreted as representing the tortuosity and

connectivity of pores with different sizes, usually given the value 0.5, re

sat r

S

(degree

of saturation), r is residual water content andsat is saturated water content and is theretention curve with matric pressure expressed as a function of water content.The parameters used in Mualems model as described above were obtained in several waysfor the data presented here (fig 1) measured water retention data were fit with the Rossi-Nimmo (1994) model, 2) measured water retention data were fit with the van Genuchten(1980) model, and 3) water retention data were estimated based on particle size distributionsand bulk density using the Rosetta model (Schaap et al., 1998).

2By Poiseuilles law the flow rate per unit cross-sectional area of a capillary tube is proportional to thesquare of the radius.


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Fig. 1. Steps used in the estimation of unsaturated hydraulic conductivity.

4. Water retention models and hydraulic conductivity estimation

The choice of the water-retention model used to produce the parameters required forhydraulic conductivity estimation also has an effect on the resulting parameters. The Rossi-

Nimmo junction (RNJ) model is one that was chosen here to fit the measurementsbecause this model is more physically realistic over the entire range of from saturation to

oven dryness (d) than other parametric models (for example Brooks and Corey, 1964 and

van Genuchten, 1980) that include the empirical, optimized residual water content (r)parameter, which is not well defined. According to capillary theory the largest pores are

associated with values near zero and drain first, followed by drainage of successively

smaller pores as approaches r. With the Brooks and Corey and van Genuchten models

there is an asymptotic approach to rmeaning that if it is taken to be >0, the number of smallpores approaches infinity at a water content above zero, which is physically unrealistic. The

curve represented by the RNJ model does not have a parameter analogous to r; thecurve goes to zeroat a fixed value of calculated for the conditions of d. The RNJ model,like many other parametric water retention models, can be analytically combined with the

capillary-bundle model of Mualem (1976) to estimateK() (Fayer and others, 1992; Rossi andNimmo, 1994; Andraski, 1996; Andraski and Jacobson, 2000).The RNJ model consists of three functions joined at two points (defined asiand j, fig. 2): a

parabolic function for the wet range of i 0), a power law function (Brooks andCorey, 1964) for the middle range of ji), and a logarithmic function for the dryrange of dj). This model has two independent parameters: (1) the scaling factorfor (o), and (2) the curve-shape parameter ( Sometimes,o is associated with atwhich air first enters a porous material during desaturation (referred to as air-entrypressure), but, actually, air begins displacing water in the largest pores at a higher (lessnegative) than oas evidenced by the departure of from saturation to the right of oonthe curve (fig. 2). Unlike the model of Brooks and Corey, which holds fixed between= 0 and the air-entry pressure, the RNJ model produces a smooth curve near saturation,represented by a parabolic function, that allows the pore-size distribution (the firstderivative of the curve) to be represented more realistically. The curve-shape parameter


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indicates the relative steepness of the middle portion of the curve, described by thepower-law function. Larger values cause the drainage portion of the curve to appearsteeper.

Fig. 2. Example of water-retention curve showing the components of the curve-fitmodel developed by Rossi and Nimmo (1994).

The parabolic function applies for i0, and is represented by:

2

1sat o

c

, (6)

where sat is saturated water content expressed volumetrically and c is a dimensionless

constant calculated from an analytical function involving the parameter (described

below) which also is dimensionless.The power law function applies for ji, and is represented by:

o

sat

. (7)

The logarithmic function applies for dj, and is represented by:

ln d

sat

, (8)


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The dependent parameters are calculated as follows:

o

d

e

,

1

2

2i o

, (9)

1

j de

,

and

2

20.52

c

.

For convenience, a dvalue of -1 107cm-water (the pressure at which the curve goes tozero ) was used in the model fits for all core samples. This is a reasonablevalue for a soildried in an oven at 105o-110oC under typical laboratory conditions (Ross and others, 1991;Rossi and Nimmo, 1994).The RNJ model is integrable in closed form for use in the Mualem (1976) hydraulic-conductivity model as described below (Rossi and Nimmo, 1994). Relative hydraulicconductivity, the ratio between the unsaturated and saturated conductivity can be expressedas:

2

2rsat sat

IK

I

, (10)

where

IIII I for 0 j ,

III I for j i , (11)

II I for i sat ,

and

1

1exp

satd

IIII

,

11

1

1

jII III j

sat sato

I I

, (12)


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2/12/12/1

112

satsat

i

o

iIII

cII

,

i i jj .

The measured water-retention data also were fit with the empirical formula of vanGenuchten (1980) which has the form:

/ 1mn

r sat r

, (13)

where , n, and mare empirical, dimensionless fitting parameters. Using measured andvalues, and nparameters are optimized to achieve the best fit to the data. The parametermis set equal to 1-1/nin order to reduce the number of independent parameters allowing

for better model convergence and to permit convenient mathematical combination withMualems model (van Genuchten, 1980) as follows

/( 1) 1 (1/ )L 2e e1 [1 ]{ }nsatK K S S n n , (14)

Where Ksat is saturated hydraulic conductivity and L is a dimensionless curve-fittingparameter.Most widely-used unsaturated flow and transport models use the van Genuchten model

rather than the Rossi-Nimmo junction model to represent . The van Genuchten equationis parameterized by sat, r, , and n, where the scaling parameter for is (analogous too) and the curve-shape parameter is n(analogous to ).

5. Hydraulic property databases

Property transfer models (PTMs) are another way to estimate unsaturated zone hydraulic

property data such as and K(). PTMs, which can be based on simple or complexrelationships among variables of interest, serve the purpose of estimating hydraulicproperties from more easily measured bulk properties such as particle size distribution andbulk density. Published databases of hydraulic properties, such as those of Holtan et al.(1968), Mualem (1976), Nemes et al. (1999), Wsten (1999), are often used in studies whendirect measurements are not possible or when data for a large number of samples arerequired, such as in development and testing of new models and theories or in comparativeor regionally extensive analyses. Some PTM development and testing studies use thesepublished databases (Vereecken et al., 1989 and 1990; Schaap et al., 1998; Hwang andPowers, 2003), while others use unpublished data or data presented only in parameterizedor graphical form (Gupta and Larson, 1979; Arya and Paris, 1981; Wagner et al., 2001).Schaap and Leij (1998) evaluated the effect of data accuracy on the uncertainty of PTMs andconcluded that the performance of a PTM depends strongly on the data being used forcalibration and testing, however, estimated properties may be sufficient depending on theapplication for which they are used.Desirable features of a database include (1) high reliability and precision of measurements,

(2) high quality, minimally disturbed samples, (3) a large and diverse sample population, (4)


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consistency in measurement techniques across the data set, (5) a full suite of hydraulic and

bulk property data for each sample, and (6) ease of use. The database of Perkins and Nimmo(2009) used for the examples in this chapter presents a data set that, though smaller in

sample number than many published databases, is ideal in several ways. Sample collection

and preparation techniques were selected to ensure minimal sample disturbance,measurements were performed by the same laboratory techniques under highly controlled

conditions, and measurements were done by a limited number of researchers. Samples arefrom diverse geographic, climatic, and geomorphic environments, and the data were

originally generated for various research purposes including recharge estimation,simulation of variably saturated flow and solute transport, theoretical studies of porous

media, and property transfer model development. Samples were from various soil depths,

including many from below the root zone. Other published data sets commonly include

samples from shallow depths; about 80% of the samples in the data set of Nemes et al. (1999)

come from depths less than 1 m. Additionally, published databases often contain

measurements done on disturbed agricultural soils. The data used here for illustrativepurposes include bulk density (b), particle density (p), particle-size distribution, saturatedhydraulic conductivity (Ksat), hydraulic conductivity as a function of water content (K()),

and water content as a function of matric potential ()).

6. Data analysis

The data used to illustrate the effect of parameterization onK() estimation and numericalflow simulations is from the database of Perkins and Nimmo (2009) described above.Specifically they are from a core sample from the unsaturated zone at the Idaho NationalLaboratory (INL) in eastern portion of the Snake River Plain. The medium is sandy in

texture with a Ksatof 3.90 x 10-3cm/s and a porosity of 0.42. Additionally, measurementsfrom 40 INL samples were used to evaluate the error inK() produced by each estimationtechnique.

6.1 Error calculationsThe root-mean-square error (RMSE), also referred to as the standard error of the estimate, isused here as a goodness-of-fit indicator between measured and predicted values ofK(). Theparameters for predicting K() were obtained using water retention data fit with the RNJmodel, the van Genuchten model, and retention parameters predicted by the Rosetta model.The RMSE is calculated as:

2

1

( )n

j jj

y y

RMSEn

, (15)

whereyj is the measured value, jis the predicted value of the dependent variable, and nisthe number of observations. Smaller values of RMSE indicate that the predicted value is

closer to the measured value of the variable.K() values span several orders of magnitudewhich, in effect, unequally weights points in the RMSE calculation, therefore the values

were logarithmically transformed prior to calculation. The number ofK() points measuredfor each sample was between three and ten.


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6.2 Parameter testing with numerical simulation

Parameterized and K() curves, representative of the modeled media, are requiredinput for numerical flow and solute transport simulations, therefore numerical simulationswere run in order to assess the influence of the input parameters on modeled results.

Utilizing parameterized unsaturated-hydraulic properties (K() and ) flow wassimulated using the U.S. Geological Survey variably-saturated two-dimensional transportmodel (VS2DT) (Lappala and others, 1983; Healy, 1990; Hsieh and others, 1999) in order toassess the effect of the chosen input parameters. The model was modified to allow for theuse of the Rossi-Nimmo water-retention parameters (Healy, personal communication 2006)in additional to the van Genuchten model parameters. VS2DT solves the finite differenceapproximation to Richards equation (Richards, 1931) for flow and the advection-dispersionequation for transport. The flow equation is written with total hydraulic potential as thedependent variable to allow straightforward treatment of both saturated and unsaturatedconditions. Several boundary conditions specific to unsaturated flow may be utilizedincluding ponded infiltration, specified fluxes in or out, seepage faces, evaporation, and

plant transpiration. As input, the model requires saturated hydraulic conductivity, porosity,parameterized unsaturated hydraulic conductivity and water-retention functions, griddelineation, and initial hydraulic conditions.Three simulations based on soil core properties are presented here. Relations betweenpressure head and water content were represented by functions developed by Rossi andNimmo and van Genuchten, in all cases using Mualems model to calculate relativehydraulic conductivity. Parameters were also obtained with the Rosetta model, as describedearlier. The 2- by 2-m domain was discretized into 1- by 1-centimeter (cm) grid blocks with aboundary condition chosen to simulate 60 minutes of infiltration at a constant rate of 0.01cm/s over a 25 cm section at the top left of the domain. Initial hydraulic conditions were

specified as uniform water content (10% volumetrically).

7. Discussion

Errors were calculated forK() for the 40 samples and ranged from 0.21 to 9.45 with the bestoverall performance achieved using the RNJ model for fitting the measured water retentiondata where 47.5% of the samples has the lowest RMSE values. The maximum RMSE valuefor the RNJ model is at least a factor of 4 lower than the other parameterizations. Onaverage, the Rosetta estimations were slightly better than those achieved by fitting themeasured water retention data using the van Genuchten model (27.5% vs. 25.0% of thesamples having the lowest RMSE values respectively). Table 1 shows the values for all 3

parameterizations for each sample.For several of the van GenuchtenK() estimates, the RMSE values were unusually large (fig.3). This occurred in cases where few data points were available and the data clusteredwithin a small range in . The van Genuchten model is not physically realistic for the entirerange of from saturation to dbecause the model uses ras an optimized parameter. Forthe particular cases where no data are available in the dry range and the measuredpoints slope steeply within a small range in , the curve asymptotically approaches rstarting from near sat. On the resultingK() curve,K decreases sharply with little change in. The) curve represented by the RNJ model goes to zero at a fixed value of calculated for the conditions of d; therefore, even when few data points are available, therelation remains somewhat realistic and, in turn, allows for a better estimate of K(. The


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RNJ model has a much narrower range in values than the other models and also producesno extreme outliers.

RMSE Values for predictedK()

Sample van Genuchtenmodel

Rossi-Nimmojunction model

Rosetta model

INEEL UZ98-2 42.98 m 0.633 0.659 0.583INEEL UZ98-2 43.09 m 0.763 0.796 0.427INEEL UZ98-2 43.21 m 0.884 0.629 0.655INEEL UZ98-2 43.31 m 1.760 0.979 8.062INEEL UZ98-2 45.21 m 0.504 0.785 0.564INEEL UZ98-2 48.16 m 0.445 0.314 1.571INEEL UZ98-2 48.26 m 0.367 0.342 1.043INEEL UZ98-2 48.44 m 1.051 0.358 0.439INEEL UZ98-2 48.92 m 0.427 0.292 1.273INEEL UZ98-2 49.02 m 0.596 0.266 1.160INEEL UZ98-2 49.23 m 1.671 0.795 0.392

INEEL UZ98-2 49.30 m 0.949 0.359 0.878INEEL UZ98-2 49.79 m 2.055 1.205 1.176INEEL UZ98-2 49.89 m 1.503 0.779 0.977INEEL UZ98-2 49.99 m 0.608 0.368 0.408INEEL UZ98-2 50.06 m 0.711 0.214 0.315INEEL UZ98-2 50.10 m 0.443 0.554 0.610INEEL UZ98-2 50.30 m 0.345 0.622 0.649ICPP-SCI-V-215 45.85 m 2.011 0.643 0.472ICPP-SCI-V-215 46.10 m 3.142 0.598 0.530ICPP-SCI-V-215 46.37 m 2.101 0.813 1.328ICPP-SCI-V-215 46.45 m 2.310 0.823 1.599ICPP-SCI-V-215 47.12 m 8.337 0.739 1.891

ICPP-SCI-V-215 47.42 m 9.451 0.564 2.103ICPP-SCI-V-215 58.36 m 3.461 2.190 1.211ICPP-SCI-V-215 58.55 m 2.598 1.293 0.863ICPP-SCI-V-215 59.20 m 0.571 0.668 1.572ICPP-SCI-V-215 59.48 m 0.743 0.596 1.365ICPP-SCI-V-215 59.70 m 5.859 1.662 0.333ICPP-SCI-V-215 59.92 m 0.841 0.568 1.959ICPP-SCI-V-189 36.59 m 0.671 0.895 2.158ICPP-SCI-V-198 42.91 m 0.776 1.068 0.415ICPP-SCI-V-204 48.41 m 0.943 1.652 3.398ICPP-SCI-V-205 42.30 m 0.610 1.085 3.802ICPP-SCI-V-213 37.91 m 1.362 1.699 0.276ICPP-SCI-V-213 56.08 m 0.787 1.620 7.624

ICPP-SCI-V-214 39.40 m 0.641 1.346 0.510ICPP-SCI-V-214 43.85 m 0.650 1.057 0.753ICPP-SCI-V-214 43.96 m 0.804 0.689 0.806ICPP-SCI-V-214 56.24 m 0.575 1.354 0.619

Average 1.624 0.848 1.419Maximum value 9.451 2.190 8.062Minimum value 0.345 0.214 0.276

Number of best fit values 10 19 11

Table 1. RMSE vales for 40 samples from the INL with water retention parameters obtainedfrom curve fitting with the van Genuchten and Rossi-Nimmo models, and estimated withthe Rosetta model.


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Fig. 3. Comparison of the RMSE values predicted hydraulic conductivity (log K) based onparameters from curves fits to water retention data with the van Genuchten and Rossi-

Nimmo models, and the Rosetta model. The box indicates the interquartile range (25th

to 75th

percentile), the red line is the median value, the whiskers indicate the values that lie within1.5 of the interquartile range, and the points indicate outliers.

Simulation results from the VS2DT model illustrate the effect of parameterization on modelresults. Figure 4 shows the hydraulic conductivity curves used in the model plotted withmeasured values.

Fig. 4. Measured and estimated hydraulic conductivity curves used in the VS2DT numericalsimulations.

The model domain, which was 2 m wide and 2 m deep, had uniform hydraulic properties(sandy textured material) and constant infiltration over a 50 cm section at the top left cornerfor 60 minutes at a rate of 0.01 cm/s. Changes in water content were output at the end of theinfiltration period at 11 observation points (fig. 5) to assess lateral and vertical watermovement.


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Fig. 5. Observation points for water content output at the end of the infiltration period.

The Rosetta parameterization, one of the most commonly used methods, had aK() RMSEof 8.06, the highest of the 3 cases. The wetting front was very diffuse compared to the othermodels and reached the 100 m vertically and laterally to 30 cm beyond the infiltrationboundary within the infiltration period (fig. 6). With the water retention curve fitting as thebasis for obtaining parameters, the maximum water content is known from the curve. TheRosetta model only has textural information therefore the porosity is estimated and thewater contents never reach the true known saturation value, which is slightly higher than

the model predicts. The van Genuchten parameterization had a K() RMSE of 1.76. Thewetting front was very sharp and progressed vertically to 60 cm with some wetting laterallyto 10 cm beyond the edge of the infiltration boundary (fig. 6). Saturation was reached more

quickly than the other 2 cases. The Rossi-Nimmo parameterization had the lowest K()RMSE of the 3 cases at 0.98. The wetting front progressed vertically about 60 cm andlaterally to 10 cm beyond the edge of the infiltration boundary (fig. 4). The results using

known retention curves with the Rossi-Nimmo and van Genuchten models to predictK()are very similar and presumably closest to reality. This analysis shows variable simulationresults due to parameterization even though the conceptual model is highly simplified andhomogeneous. The effects of soil structure, layering, preferential flow, variable water inputs,nonuniform initial moisture conditions, and other mechanisms that are often found to

dominate field situations are not considered here. These effects would further complicatethe model uncertainty as influenced by the chosen parameter estimation method in waysthat may be difficult to anticipate.The extremely simplified type of analysis presented here assumes that flow through theunsaturated zone proceeds as described by the Richards equation. Many studies show thatthere are processes, such as preferential flow, that are not adequately described by Richardsequation (Perkins et al., 2011; Tyner et al., 2006; Khne and Gerke, 2005; Jaynes et al., 2001;Yoder, 2001; Iragavarapu et al., 1998, Flury et al., 1994). There are recent studies suggestingthat hydraulic conductivity and water retention may be important for modeling diffusematrix flow; however, they may not capture some of the dominant field-scale processes suchas preferential flow. These processes may be better represented by the addition of


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parameters related to the nature of the water input source and preferential flow path densitywhich will improve the capability of unsaturated zone flow models (Nimmo, 2007; Nimmo2010). The examples given here show that model results are highly sensitive to the estimatedparameters. It is also certain that the use of field-measured (small or large scale), laboratory-

measured, and empirically-estimated data in numerical models will yield significantlydifferent results. Another important aspect to consider in evaluating unsaturated zone flowis whether or not the numerical model can accurately represent all of the processes in theconceptual model which should be based on field observations to the extent possible (e.g.information about soil structure, macropores, anthropogenic modifications, etc.).

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terContent(vol/vol)

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0.100.15

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Time (s)

X=20, Z=10

X=40, Z=10

X=60, Z=10

X=80, Z=10

X=100, Z=10

Rosetta parameters

van Genuchten parameters

Rossi-Nimmo parameters

X=20, Z=10

X=40, Z=10

X=60, Z=10

X=80, Z=10

X=100, Z=10

X=120, Z=10

Lateral watercontent changes

Vertical watercontent changes

Fig. 6. Water contents siimulated for the simple infiltration model using the VS2DT model.


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8. Summary and conclusions

Understanding the highly nonlinear relationship between water content and hydraulicconductivity is one element in predicting water flow and solute transport processes in the

unsaturated zone. Measurement of unsaturated hydraulic conductivity of sediments iscostly and time consuming, therefore use of models that estimate this property from moreeasily measured bulk-physical properties is common. In hydrologic studies, especially thoseusing dynamic unsaturated zone moisture modeling, calculations based on propertytransfer models informed by hydraulic property databases are often used in lieu ofmeasured data from the site of interest. The degree to which the unsaturated hydraulicconductivity curves estimated from property-transfer-modeled water-retention parametersand saturated hydraulic conductivity approximate the laboratory-measured data wereevaluated. Results indicate that using the physically realistic water retention model of Rossiand Nimmo (1994) yields results that are closer to measured values especially wheremeasured data are sparse. Using the Rosetta pedotransfer model or the van Genuchten

water retention model produced about the same goodness of fit between the measured andmodeled hydraulic conductivity data. Because numerical models of variably-saturatedsolute transport require parameterized hydraulic properties as input, simulation resultswere shown to illustrate the effect of the various parameters on model performance. It isclear that the model results vary widely for a highly simple conceptual model and it is likelythat the addition of more physically realistic characteristics would further affect the modelperformance in complex ways.

9. References

Andraski, B.J., 1996, Properties and variability of soil and trench fill at an arid waste-burial

site: Soil Science Society of America Journal, v. 60, p. 5466.Andraski, B.J., & E.A. Jacobson, 2000, Testing a full-range soil-water retention function in

modeling water potential and temperature: Water Resources Research, v. 36, no. 10,p. 30813089.

Arya L.M., & J.F. Paris, 1981, A physicoempirical model to predict the soil moisturecharacteristic from particle-size distribution and bulk density data, Soil Sc.i Soc.Am. J. 45:6 1023-1030.

Brooks R.H., & A.T. Corey, 1964, Hydraulic properties of porous media, Colorado StateUniversity Hydrology Paper 3, 27 p.

Campbell G.S., & G.W. Gee, 1986, Water potential: miscellaneous methods, In Methods ofsoil analysis, part IPhysical and mineralogical methods (second edition), Soil Sci.

Soc. Am. Book Series No. 9, Madison, Wisconsin, edited by A. Klute, pp 628-630.Conca J.L., & J.V. Wright, 1998, The UFA method for rapid, direct measurement of

unsaturated transport properties in soil, sediment, and rock, Aust. J. Soil Res. 36:291-315.

Fawcett R.G., & N. Collis-George, 1967, A filter paper method for determining the moisturecharacteristics of soil. Aust. .J Exper. Ag. and Anim. Hu.s 7(24):162-167.

Fayer, M.J., M.L. Rockhold, & M.D. Campbell, 1992, Hydrologic modeling of protectivebarriersComparison of field data and simulation results: Soil Science Society ofAmerica Journal, v. 56, p. 690700.


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